/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([1, -6, 3, 10, -3, -3, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([37, 37, w^4 - 2*w^3 - 3*w^2 + 3*w + 2]) primes_array = [ [3, 3, w - 1],\ [17, 17, -w^2 + 2*w + 1],\ [17, 17, -w^3 + w^2 + 4*w],\ [19, 19, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + w - 4],\ [19, 19, w^2 - w - 1],\ [37, 37, w^4 - 2*w^3 - 3*w^2 + 3*w + 2],\ [37, 37, w^4 - 4*w^3 + w^2 + 7*w - 3],\ [53, 53, 2*w^5 - 6*w^4 - 6*w^3 + 18*w^2 + 9*w - 6],\ [53, 53, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - 3*w + 2],\ [64, 2, -2],\ [71, 71, -w^5 + 4*w^4 - w^3 - 8*w^2 + 3*w - 1],\ [71, 71, 2*w^5 - 5*w^4 - 8*w^3 + 15*w^2 + 12*w - 6],\ [71, 71, 2*w^5 - 6*w^4 - 6*w^3 + 18*w^2 + 9*w - 7],\ [73, 73, -2*w^5 + 6*w^4 + 5*w^3 - 16*w^2 - 7*w + 3],\ [73, 73, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 6*w + 6],\ [89, 89, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 8*w - 4],\ [89, 89, w^5 - w^4 - 9*w^3 + 7*w^2 + 16*w - 6],\ [89, 89, 2*w^5 - 6*w^4 - 4*w^3 + 15*w^2 + 3*w - 3],\ [89, 89, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 10*w - 6],\ [107, 107, w^5 - 2*w^4 - 7*w^3 + 10*w^2 + 12*w - 6],\ [107, 107, 2*w^5 - 5*w^4 - 7*w^3 + 14*w^2 + 9*w - 5],\ [107, 107, w^5 - 3*w^4 - 3*w^3 + 9*w^2 + 6*w - 3],\ [107, 107, w^4 - 2*w^3 - 3*w^2 + 4*w + 1],\ [109, 109, 2*w^5 - 5*w^4 - 8*w^3 + 15*w^2 + 13*w - 6],\ [109, 109, -w^4 + 4*w^3 - w^2 - 9*w + 3],\ [127, 127, w^4 - 3*w^3 + 5*w - 4],\ [127, 127, -w^5 + 3*w^4 + w^3 - 6*w^2 + w + 3],\ [127, 127, 2*w^5 - 5*w^4 - 8*w^3 + 16*w^2 + 11*w - 6],\ [127, 127, w^5 - 4*w^4 + 2*w^3 + 7*w^2 - 7*w],\ [163, 163, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w + 5],\ [163, 163, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 2*w + 5],\ [163, 163, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 8*w + 4],\ [163, 163, w^5 - 4*w^4 + 10*w^2 - w - 4],\ [179, 179, -w^5 + 3*w^4 + 3*w^3 - 7*w^2 - 7*w - 1],\ [179, 179, 2*w^5 - 6*w^4 - 5*w^3 + 18*w^2 + 5*w - 7],\ [179, 179, -2*w^5 + 5*w^4 + 10*w^3 - 19*w^2 - 18*w + 10],\ [179, 179, -2*w^5 + 5*w^4 + 9*w^3 - 17*w^2 - 14*w + 9],\ [197, 197, 2*w^5 - 6*w^4 - 5*w^3 + 18*w^2 + 3*w - 7],\ [197, 197, -w^5 + 4*w^4 - w^3 - 7*w^2 + 3*w - 2],\ [197, 197, w^5 - w^4 - 7*w^3 + 4*w^2 + 10*w - 3],\ [197, 197, -2*w^5 + 8*w^4 - 2*w^3 - 17*w^2 + 10*w + 1],\ [197, 197, -w^4 + 3*w^3 + 2*w^2 - 6*w - 2],\ [197, 197, w^5 - 4*w^4 + w^3 + 9*w^2 - 4*w - 2],\ [199, 199, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 10*w + 4],\ [199, 199, -w^4 + 3*w^3 + 2*w^2 - 9*w + 1],\ [233, 233, 2*w^5 - 4*w^4 - 12*w^3 + 17*w^2 + 19*w - 9],\ [233, 233, -w^5 + w^4 + 8*w^3 - 6*w^2 - 13*w + 6],\ [233, 233, 2*w^5 - 6*w^4 - 6*w^3 + 19*w^2 + 9*w - 7],\ [233, 233, w^5 - 4*w^4 + 11*w^2 - 4*w - 2],\ [251, 251, -2*w^5 + 5*w^4 + 10*w^3 - 18*w^2 - 18*w + 7],\ [251, 251, w^3 - w^2 - 3*w - 2],\ [251, 251, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 3*w - 3],\ [251, 251, -w^5 + 4*w^4 - 11*w^2 + 4*w + 3],\ [269, 269, w^5 - 3*w^4 - w^3 + 6*w^2 - 2*w - 3],\ [269, 269, 2*w^5 - 7*w^4 - 3*w^3 + 20*w^2 + 3*w - 8],\ [271, 271, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 7],\ [271, 271, -w^4 + 4*w^3 - w^2 - 10*w + 6],\ [289, 17, -w^5 + 3*w^4 + w^3 - 5*w^2 - 2],\ [289, 17, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 6*w - 4],\ [307, 307, 2*w^5 - 5*w^4 - 10*w^3 + 19*w^2 + 16*w - 8],\ [307, 307, w^5 - 4*w^4 + 2*w^3 + 7*w^2 - 6*w - 1],\ [307, 307, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 3*w + 2],\ [307, 307, w^5 - 2*w^4 - 6*w^3 + 10*w^2 + 7*w - 9],\ [361, 19, 2*w^5 - 6*w^4 - 6*w^3 + 18*w^2 + 8*w - 5],\ [361, 19, w^5 - 3*w^4 - w^3 + 5*w^2 + 3],\ [379, 379, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 9*w - 5],\ [379, 379, -2*w + 3],\ [397, 397, -w^5 + 5*w^4 - 6*w^3 - 6*w^2 + 14*w - 5],\ [397, 397, -w^5 + 3*w^4 + w^3 - 4*w^2 - w - 5],\ [397, 397, 3*w^5 - 9*w^4 - 7*w^3 + 23*w^2 + 9*w - 6],\ [397, 397, -w^4 + 5*w^3 - 2*w^2 - 10*w + 1],\ [431, 431, -3*w^5 + 8*w^4 + 11*w^3 - 24*w^2 - 18*w + 9],\ [431, 431, 2*w^5 - 6*w^4 - 3*w^3 + 13*w^2 + w - 3],\ [431, 431, -3*w^5 + 8*w^4 + 10*w^3 - 23*w^2 - 14*w + 8],\ [431, 431, -2*w^5 + 6*w^4 + 4*w^3 - 14*w^2 - 5*w],\ [433, 433, -3*w^5 + 9*w^4 + 8*w^3 - 25*w^2 - 11*w + 9],\ [433, 433, -2*w^5 + 6*w^4 + 4*w^3 - 16*w^2 - 3*w + 7],\ [433, 433, 2*w^5 - 5*w^4 - 7*w^3 + 13*w^2 + 11*w - 4],\ [433, 433, -w^4 + 4*w^3 + w^2 - 10*w - 2],\ [449, 449, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 + w + 3],\ [449, 449, -w^4 + 4*w^3 - 2*w^2 - 5*w + 5],\ [449, 449, -w^5 + 4*w^4 - w^3 - 8*w^2 + 3*w - 2],\ [449, 449, -w^3 + 5*w + 3],\ [449, 449, w^3 - 5*w],\ [449, 449, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - w - 6],\ [467, 467, -2*w^4 + 7*w^3 - 16*w + 7],\ [467, 467, -2*w^4 + 6*w^3 + w^2 - 10*w + 3],\ [487, 487, -w^5 + 2*w^4 + 6*w^3 - 10*w^2 - 8*w + 9],\ [487, 487, 2*w^5 - 6*w^4 - 5*w^3 + 15*w^2 + 7*w - 3],\ [487, 487, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 8*w - 6],\ [487, 487, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 8*w + 1],\ [503, 503, 2*w^5 - 7*w^4 - 3*w^3 + 19*w^2 + 3*w - 6],\ [503, 503, 2*w^5 - 6*w^4 - 5*w^3 + 18*w^2 + 4*w - 6],\ [503, 503, 2*w^5 - 5*w^4 - 9*w^3 + 17*w^2 + 13*w - 7],\ [503, 503, -w^5 + 4*w^4 - 10*w^2 + 3*w - 1],\ [521, 521, w^5 - 4*w^4 + 11*w^2 - w - 6],\ [521, 521, w^5 - w^4 - 9*w^3 + 8*w^2 + 15*w - 6],\ [521, 521, -w^5 + 4*w^4 - 2*w^3 - 8*w^2 + 9*w],\ [521, 521, -2*w^5 + 4*w^4 + 11*w^3 - 15*w^2 - 17*w + 9],\ [523, 523, 3*w^5 - 8*w^4 - 10*w^3 + 24*w^2 + 12*w - 10],\ [523, 523, -w^4 + 3*w^3 - w^2 - 4*w + 5],\ [523, 523, -2*w^5 + 4*w^4 + 11*w^3 - 14*w^2 - 17*w + 7],\ [523, 523, -w^5 + 5*w^4 - 4*w^3 - 9*w^2 + 9*w + 1],\ [577, 577, -3*w^5 + 8*w^4 + 10*w^3 - 22*w^2 - 14*w + 7],\ [577, 577, -2*w^5 + 7*w^4 + w^3 - 15*w^2 + 2*w + 2],\ [593, 593, 2*w^5 - 5*w^4 - 9*w^3 + 17*w^2 + 15*w - 10],\ [593, 593, w^3 - w^2 - 2*w - 2],\ [593, 593, -3*w^5 + 9*w^4 + 9*w^3 - 27*w^2 - 14*w + 10],\ [593, 593, 2*w^5 - 6*w^4 - 6*w^3 + 19*w^2 + 8*w - 7],\ [613, 613, w^5 - 2*w^4 - 7*w^3 + 9*w^2 + 12*w - 5],\ [613, 613, w^5 - w^4 - 9*w^3 + 8*w^2 + 13*w - 7],\ [613, 613, w^5 - 5*w^4 + 3*w^3 + 11*w^2 - 6*w - 2],\ [613, 613, -w^4 + 3*w^3 + w^2 - 5*w + 4],\ [613, 613, w^5 - w^4 - 9*w^3 + 7*w^2 + 14*w - 4],\ [613, 613, w^5 - 2*w^4 - 7*w^3 + 11*w^2 + 12*w - 8],\ [631, 631, 2*w^5 - 7*w^4 + 15*w^2 - 6*w - 2],\ [631, 631, -3*w^5 + 8*w^4 + 10*w^3 - 23*w^2 - 12*w + 10],\ [631, 631, w^5 - 3*w^4 + w^3 + 3*w^2 - 6*w + 3],\ [631, 631, -3*w^5 + 8*w^4 + 13*w^3 - 29*w^2 - 21*w + 15],\ [683, 683, -w^5 + 4*w^4 - w^3 - 8*w^2 + 2*w - 1],\ [683, 683, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 11*w - 4],\ [701, 701, -w^5 + 3*w^4 + w^3 - 7*w^2 + 3*w + 2],\ [701, 701, 2*w^2 - 3*w - 4],\ [719, 719, 2*w^5 - 5*w^4 - 8*w^3 + 16*w^2 + 13*w - 8],\ [719, 719, w^5 - 5*w^4 + 4*w^3 + 10*w^2 - 10*w - 1],\ [719, 719, w^5 - w^4 - 9*w^3 + 6*w^2 + 16*w - 2],\ [719, 719, 2*w^5 - 5*w^4 - 9*w^3 + 18*w^2 + 15*w - 10],\ [739, 739, -2*w^5 + 9*w^4 - 6*w^3 - 15*w^2 + 16*w - 7],\ [739, 739, 4*w^5 - 9*w^4 - 19*w^3 + 30*w^2 + 28*w - 14],\ [757, 757, 2*w^5 - 5*w^4 - 9*w^3 + 16*w^2 + 17*w - 7],\ [757, 757, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 6*w - 6],\ [757, 757, 2*w^5 - 6*w^4 - 7*w^3 + 20*w^2 + 11*w - 6],\ [757, 757, -2*w^4 + 5*w^3 + 4*w^2 - 10*w - 1],\ [773, 773, 2*w^5 - 8*w^4 + 3*w^3 + 16*w^2 - 11*w],\ [773, 773, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 12*w - 6],\ [809, 809, 2*w^5 - 6*w^4 - 3*w^3 + 13*w^2 + 2*w - 3],\ [809, 809, -2*w^3 + 5*w^2 + 4*w - 6],\ [811, 811, -w^4 + 3*w^3 + 3*w^2 - 7*w - 3],\ [811, 811, 2*w^5 - 7*w^4 - w^3 + 17*w^2 - 3*w - 6],\ [827, 827, w^5 - 4*w^4 + w^3 + 10*w^2 - 5*w - 4],\ [827, 827, w^5 - 4*w^4 + w^3 + 10*w^2 - 5*w - 5],\ [829, 829, 2*w^5 - 4*w^4 - 11*w^3 + 15*w^2 + 18*w - 9],\ [829, 829, 2*w^5 - 6*w^4 - 7*w^3 + 19*w^2 + 13*w - 7],\ [829, 829, -2*w^5 + 9*w^4 - 5*w^3 - 18*w^2 + 15*w],\ [829, 829, 3*w^5 - 9*w^4 - 9*w^3 + 28*w^2 + 11*w - 11],\ [829, 829, w^3 - 2*w^2 - 3*w - 1],\ [829, 829, -2*w^5 + 4*w^4 + 12*w^3 - 17*w^2 - 20*w + 10],\ [863, 863, -w^4 + 4*w^3 + w^2 - 11*w],\ [863, 863, w^4 - 4*w^3 - w^2 + 11*w + 1],\ [919, 919, -w^5 + 5*w^4 - 3*w^3 - 11*w^2 + 4*w + 1],\ [919, 919, -w^5 + 4*w^4 - w^3 - 8*w^2 + 6*w - 4],\ [919, 919, -w^4 + 5*w^3 - w^2 - 12*w + 1],\ [919, 919, -2*w^5 + 5*w^4 + 7*w^3 - 13*w^2 - 11*w + 6],\ [937, 937, 2*w^5 - 6*w^4 - 3*w^3 + 12*w^2 + 3*w],\ [937, 937, 2*w^5 - 4*w^4 - 10*w^3 + 12*w^2 + 16*w - 5],\ [937, 937, w^5 - 4*w^4 + 8*w^2 + w + 1],\ [937, 937, 2*w^4 - 8*w^3 + 2*w^2 + 16*w - 5],\ [953, 953, -w^5 + 4*w^4 - 11*w^2 + 3*w + 7],\ [953, 953, w^5 - 2*w^4 - 7*w^3 + 9*w^2 + 13*w - 7],\ [953, 953, -w^5 + 3*w^4 + w^3 - 7*w^2 + 4*w + 1],\ [953, 953, 2*w^5 - 8*w^4 + 3*w^3 + 16*w^2 - 11*w - 1],\ [971, 971, w^4 - w^3 - 5*w^2 + 2*w + 4],\ [971, 971, -w^4 + w^3 + 4*w^2 - w + 1],\ [971, 971, -2*w^5 + 5*w^4 + 10*w^3 - 20*w^2 - 15*w + 9],\ [971, 971, w^4 - 2*w^3 - 4*w^2 + 6*w + 1],\ [991, 991, -w - 3],\ [991, 991, -2*w^5 + 7*w^4 + 3*w^3 - 19*w^2 - 5*w + 6],\ [991, 991, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - 5*w + 7],\ [991, 991, 2*w^5 - 7*w^4 - 2*w^3 + 16*w^2 + 2*w],\ [1009, 1009, 2*w^4 - 6*w^3 - 2*w^2 + 11*w],\ [1009, 1009, -w^5 + w^4 + 9*w^3 - 7*w^2 - 15*w + 6],\ [1061, 1061, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 4*w + 2],\ [1061, 1061, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + 2*w - 7],\ [1063, 1063, 2*w^5 - 5*w^4 - 10*w^3 + 18*w^2 + 18*w - 9],\ [1063, 1063, -2*w^5 + 5*w^4 + 8*w^3 - 15*w^2 - 14*w + 8],\ [1063, 1063, -w^5 + 4*w^4 - 11*w^2 + 4*w + 5],\ [1063, 1063, w^5 - 2*w^4 - 7*w^3 + 10*w^2 + 14*w - 5],\ [1117, 1117, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 7*w + 5],\ [1117, 1117, -w^5 + 2*w^4 + 3*w^3 - 2*w^2 - 3*w - 3],\ [1117, 1117, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 5*w - 8],\ [1117, 1117, w^5 - 4*w^4 + 3*w^3 + 4*w^2 - 7*w + 4],\ [1151, 1151, -w^4 + 4*w^3 - 10*w - 1],\ [1151, 1151, w^5 - 3*w^4 - w^3 + 8*w^2 - 3*w - 3],\ [1151, 1151, 3*w^5 - 8*w^4 - 8*w^3 + 19*w^2 + 8*w - 3],\ [1151, 1151, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 12*w - 5],\ [1171, 1171, w^5 - 2*w^4 - 5*w^3 + 5*w^2 + 7*w + 1],\ [1171, 1171, 3*w^5 - 10*w^4 - 4*w^3 + 25*w^2 + 3*w - 7],\ [1171, 1171, -w^5 + 5*w^4 - 3*w^3 - 11*w^2 + 8*w + 3],\ [1171, 1171, -2*w^5 + 5*w^4 + 7*w^3 - 16*w^2 - 7*w + 6],\ [1187, 1187, -3*w^5 + 8*w^4 + 12*w^3 - 27*w^2 - 18*w + 11],\ [1187, 1187, w^4 - 2*w^3 - 2*w^2 + 4*w - 3],\ [1259, 1259, 2*w^5 - 6*w^4 - 5*w^3 + 16*w^2 + 9*w - 5],\ [1259, 1259, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 9*w - 7],\ [1277, 1277, -3*w^5 + 11*w^4 + w^3 - 25*w^2 + 2*w + 3],\ [1277, 1277, -w^4 + w^3 + 5*w^2 - w - 6],\ [1277, 1277, 2*w^5 - 6*w^4 - 4*w^3 + 13*w^2 + 5*w + 1],\ [1277, 1277, w^4 - 5*w^3 + 3*w^2 + 9*w - 7],\ [1277, 1277, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - 4*w - 1],\ [1277, 1277, 3*w^5 - 9*w^4 - 6*w^3 + 22*w^2 + 5*w - 4],\ [1279, 1279, -2*w^5 + 4*w^4 + 12*w^3 - 17*w^2 - 18*w + 11],\ [1279, 1279, -3*w^5 + 11*w^4 - 23*w^2 + 5*w + 2],\ [1279, 1279, w^3 + w^2 - 5*w - 2],\ [1279, 1279, -2*w^5 + 6*w^4 + 7*w^3 - 21*w^2 - 9*w + 9],\ [1279, 1279, -w^5 + 3*w^4 + 5*w^3 - 12*w^2 - 9*w + 4],\ [1279, 1279, -2*w^3 + 5*w^2 + 3*w - 8],\ [1297, 1297, -2*w^5 + 4*w^4 + 11*w^3 - 14*w^2 - 19*w + 7],\ [1297, 1297, -w^5 + w^4 + 10*w^3 - 9*w^2 - 19*w + 7],\ [1331, 11, -3*w^5 + 7*w^4 + 16*w^3 - 26*w^2 - 28*w + 9],\ [1331, 11, w^3 - w^2 - w - 3],\ [1367, 1367, 2*w^5 - 6*w^4 - 4*w^3 + 13*w^2 + 5*w],\ [1367, 1367, w^3 - 6*w],\ [1367, 1367, 3*w^5 - 9*w^4 - 6*w^3 + 22*w^2 + 5*w - 5],\ [1367, 1367, w^3 - 6*w - 2],\ [1369, 37, 2*w^5 - 6*w^4 - 7*w^3 + 20*w^2 + 10*w - 8],\ [1369, 37, 3*w^5 - 9*w^4 - 8*w^3 + 25*w^2 + 10*w - 8],\ [1423, 1423, 3*w^5 - 10*w^4 - 5*w^3 + 26*w^2 + 6*w - 3],\ [1423, 1423, -2*w^4 + 7*w^3 - w^2 - 13*w + 4],\ [1459, 1459, -w^5 + 4*w^4 - 3*w^3 - 4*w^2 + 8*w - 5],\ [1459, 1459, 2*w^5 - 5*w^4 - 6*w^3 + 11*w^2 + 8*w],\ [1459, 1459, -2*w^5 + 7*w^4 + 4*w^3 - 22*w^2 - 2*w + 7],\ [1459, 1459, -3*w^5 + 8*w^4 + 14*w^3 - 29*w^2 - 24*w + 11],\ [1493, 1493, -3*w^5 + 9*w^4 + 9*w^3 - 25*w^2 - 16*w + 6],\ [1493, 1493, -2*w^5 + 3*w^4 + 15*w^3 - 14*w^2 - 27*w + 9],\ [1493, 1493, w^5 - 4*w^4 + 2*w^3 + 5*w^2 - 5*w + 3],\ [1493, 1493, -3*w^5 + 8*w^4 + 9*w^3 - 21*w^2 - 11*w + 7],\ [1531, 1531, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 + w + 4],\ [1531, 1531, 2*w^5 - 6*w^4 - 6*w^3 + 17*w^2 + 11*w - 7],\ [1549, 1549, w^5 - 4*w^4 - 3*w^3 + 14*w^2 + 7*w - 4],\ [1549, 1549, -4*w^5 + 10*w^4 + 18*w^3 - 34*w^2 - 28*w + 15],\ [1567, 1567, -3*w^5 + 6*w^4 + 17*w^3 - 23*w^2 - 25*w + 9],\ [1567, 1567, -w^5 + 3*w^4 + 6*w^3 - 13*w^2 - 12*w + 4],\ [1583, 1583, w^5 - 2*w^4 - 8*w^3 + 11*w^2 + 15*w - 7],\ [1583, 1583, w^5 - 4*w^4 - w^3 + 13*w^2 - w - 7],\ [1601, 1601, -w^4 + 4*w^3 - 3*w^2 - 6*w + 7],\ [1601, 1601, 3*w^5 - 8*w^4 - 9*w^3 + 22*w^2 + 10*w - 8],\ [1619, 1619, 2*w^5 - 5*w^4 - 11*w^3 + 19*w^2 + 21*w - 6],\ [1619, 1619, w^5 - 2*w^4 - 8*w^3 + 13*w^2 + 12*w - 12],\ [1619, 1619, -4*w^5 + 9*w^4 + 20*w^3 - 32*w^2 - 31*w + 13],\ [1619, 1619, w^5 - 2*w^4 - 6*w^3 + 10*w^2 + 10*w - 12],\ [1637, 1637, -w^5 + 2*w^4 + 4*w^3 - 4*w^2 - 5*w - 3],\ [1637, 1637, w^5 - 4*w^4 + 2*w^3 + 6*w^2 - 5*w + 4],\ [1637, 1637, 4*w^5 - 10*w^4 - 17*w^3 + 31*w^2 + 29*w - 12],\ [1637, 1637, -w^5 + 5*w^4 - 5*w^3 - 8*w^2 + 15*w - 1],\ [1657, 1657, w^4 - 2*w^3 - w^2 + w - 4],\ [1657, 1657, 2*w^5 - 5*w^4 - 8*w^3 + 17*w^2 + 9*w - 7],\ [1693, 1693, w^5 - 2*w^4 - 9*w^3 + 14*w^2 + 15*w - 8],\ [1693, 1693, w^5 - 3*w^4 - 3*w^3 + 9*w^2 + w],\ [1709, 1709, 2*w^5 - 7*w^4 - 3*w^3 + 18*w^2 + 4*w - 3],\ [1709, 1709, 3*w^5 - 8*w^4 - 11*w^3 + 25*w^2 + 14*w - 9],\ [1709, 1709, -w^5 + w^4 + 11*w^3 - 11*w^2 - 20*w + 9],\ [1709, 1709, -w^5 + w^4 + 7*w^3 - 3*w^2 - 12*w + 1],\ [1747, 1747, -w^5 + 5*w^4 - 3*w^3 - 9*w^2 + 7*w - 4],\ [1747, 1747, -3*w^5 + 11*w^4 - 24*w^2 + 5*w + 3],\ [1783, 1783, -w^4 + 3*w^3 + 2*w^2 - 5*w - 4],\ [1783, 1783, -2*w^5 + 7*w^4 + 2*w^3 - 18*w^2 - w + 4],\ [1871, 1871, -w^5 + 3*w^4 + 4*w^3 - 11*w^2 - 9*w + 6],\ [1871, 1871, 2*w^5 - 8*w^4 + w^3 + 17*w^2 - 3*w - 2],\ [1871, 1871, 2*w^5 - 6*w^4 - 5*w^3 + 16*w^2 + 9*w - 6],\ [1871, 1871, -3*w^5 + 11*w^4 - w^3 - 23*w^2 + 12*w - 3],\ [1873, 1873, -w^5 + w^4 + 8*w^3 - 5*w^2 - 11*w + 4],\ [1873, 1873, 3*w^5 - 6*w^4 - 15*w^3 + 19*w^2 + 22*w - 9],\ [1889, 1889, 2*w^5 - 5*w^4 - 8*w^3 + 14*w^2 + 13*w - 5],\ [1889, 1889, -2*w^5 + 5*w^4 + 8*w^3 - 15*w^2 - 12*w + 8],\ [1889, 1889, 2*w^5 - 7*w^4 - w^3 + 16*w^2 - 3*w - 5],\ [1889, 1889, w^5 - 4*w^4 + w^3 + 8*w^2 - 4*w - 3],\ [1907, 1907, -3*w^5 + 6*w^4 + 18*w^3 - 25*w^2 - 28*w + 12],\ [1907, 1907, 2*w^5 - 5*w^4 - 7*w^3 + 14*w^2 + 8*w - 1],\ [1979, 1979, 2*w^4 - 9*w^3 + 5*w^2 + 18*w - 11],\ [1979, 1979, 4*w^5 - 10*w^4 - 14*w^3 + 27*w^2 + 20*w - 8],\ [1997, 1997, 3*w^5 - 8*w^4 - 11*w^3 + 25*w^2 + 14*w - 10],\ [1997, 1997, -4*w^5 + 13*w^4 + 5*w^3 - 32*w^2 + w + 4],\ [1997, 1997, 2*w^5 - 7*w^4 - 3*w^3 + 18*w^2 + 4*w - 4],\ [1997, 1997, -4*w^5 + 11*w^4 + 15*w^3 - 35*w^2 - 24*w + 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-3, 3, -3, 2, 5, 1, -10, 12, -12, -1, 9, -12, -12, -7, 2, -6, -15, 12, 12, 0, -3, 18, 0, -13, 14, -16, -1, -7, 11, -16, -19, 2, -19, 15, 18, -12, 0, 3, -12, 3, 0, 6, -15, -13, -4, -6, 18, 18, 24, -15, -15, -3, 6, 18, 0, -28, -25, -4, -10, 20, -4, 2, 20, -25, 17, 11, -28, 29, -10, -10, 20, -30, -24, -36, 0, 20, -28, -16, 38, -27, 30, -3, 12, 15, 30, -21, 18, 11, 11, -13, -7, -12, -12, 24, -18, -15, -30, 3, 42, -16, -16, -19, -34, -25, 11, -30, 9, 36, 18, -22, 32, 2, 14, -28, 38, 23, -34, 26, 20, -21, -24, -27, -39, -30, 39, 21, 48, 8, -25, -34, -22, 44, 2, -18, -33, -6, -15, -16, 8, 3, 27, 20, 26, 11, 20, -37, 11, -24, -48, -40, 29, 8, -10, -37, -52, -16, -25, -42, -15, -27, -57, -39, 33, 6, 6, -52, 32, -22, -46, 35, 2, 42, -27, 14, -7, 2, -16, 11, -49, 2, -58, 24, -42, -48, -18, 38, -16, -4, -40, 36, 18, 33, -27, -15, 18, 21, 54, -24, 24, -25, -10, -40, -7, -61, -52, -1, 2, 54, -18, 21, -15, -24, 66, -1, -22, 14, 56, -16, -40, 17, 56, -33, -72, 57, 27, 50, -28, -1, 17, -34, -25, -48, -57, 0, 51, -30, -33, 18, 36, 18, 63, -6, 33, 62, -49, -52, 29, 54, 18, -30, 6, 20, -40, -64, 74, -63, -72, 27, -21, -46, 11, -6, 6, 18, 57, 3, -45, -84, 78, -33, 3, -3, -27] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([37, 37, w^4 - 2*w^3 - 3*w^2 + 3*w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]